What is the easiest way to convert the gray-code output from a Bourns optical encoder to binary (parallell)?
I don't want to use a microcontroller. Perhaps there is a IC that converts from gray code to binary that I can use?

Perhaps using a simple prom/eprom device would suffice - feed the gray code output of the optical encoder (buffered to correct voltage if not 5v) onto the address pins of the prom, take the translated binary value (upto 8 bits) from the data pins.

Feed the Gray MSB directly through to be your Binary MSB.
Then make an XOR of the the Gray MSB and 2.MSB. Output will be your Binay 2.MSB.
Then XOR this output with your Gray 3rd. MSB.
Output is now your 3. MSB Binary.
Proceed with XORing each output with your next following unused Gray bit until your all done.
That's all there is to it.
On the other hand, - generating a LUT in a PROM might do it in one chip, as 8 bits will need two XOR DIPs.
One DIP will suffice up to 7 Gray bits...........